What is unpolarized light? -A light wave is an electromagnetic wave that travels through a vacuum. Vibrating electric charges produce light waves. An electromagnetic wave has both an electric and a magnetic component. A light wave that is vibrating in more than one plane is unpolarized light.
What is polarized light and polarization? -Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. There are four methods: transmission, reflection, refraction, and scattering. In transmission through a Polaroid filter, light emerges with one-half the intensity and with vibrations in a single plane (as unpolarized light). Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces. Polarization is dependent upon the angle at which the light approaches the surface and upon the material that the surface is made of. Refraction occurs when a beam of light passes from one material into another material. The path of the beam changes its direction at the contact between both materials. The refracted beam acquires some polarization. The polarization occurs in a plane perpendicular to the surface. Polarization also occurs when light is scattered while traveling through a medium. When light strikes the atoms of a material, it will often set the electrons of those atoms into vibration. The vibrating electrons then produce their own electromagnetic wave that is radiated outward in all directions.
Summary Lesson 2A
What are electromagnetic and visible spectra? Electromagnetic waves exist with an enormous range of frequencies, known as the electromagnetic spectrum. Our eyes are sensitive to only the visible light spectrum. Each color is characteristic to a different wavelength; and different wavelengths of light waves will bend varying amounts upon passage through a prism. When all the wavelengths of the visible light spectrum strike your eye at the same time, white is perceived. Visible light - the mix of ROYGBIV - is referred to as white light.
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Summary Lesson 1A-D
What is the role of light to sight?Without light, there wouldn’t be sight. We are able to see because light from an object can move through space and reach our eyes.Luminous objects are objects that generate their own light. Illuminated objects are objects that are capable of reflecting light to our eyes. Humans are illuminated objects like the moon. What is the line of sight? Directing our sight in a specific direction is known the line of sight. To view an object, one must see along a line at that object; and when you do light will come from that object to your eye along the line of sight. Although this light diverges from the object in a variety of directions, your eye only sees the very small diverging cone of rays that is coming towards it. The light ray approaching the mirror is the incident ray. The light ray that reflects off of the mirror and travels to our rye is the reflected ray. The distance from the mirror to the object (object distance) is equal to the distance from the mirror to the image (image distance).
What is the law of reflection?Behavior of light is very predictable. The normal line divides the angle between the incident ray and the reflected ray into two equal angles.
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What is the difference between specular and diffuse reflection?The law of reflection is always observed, regardless of the orientation of the surface. Reflection off of smooth surfaces such as mirrors or a calm body of water leads to specular reflection. Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to diffuse reflection.
Summary Lesson 2
Why is an image formed? In order to see the image of an object in a mirror, you must sight at the image; when you sight at the image, light will come to your eye along that line of sight. The image location is thus located at that position where observers are sighting when viewing the image of an object. It is the location behind the mirror where all the light appears to diverge from.
What are image characteristics in plane mirrors? Characteristics include type, size, orientation, location. Type can either be real or virtual, real being the actually light where it seems to be and virtual being behind the mirror or in front of the lens. Size can be enlarged, unchanged, or reduced. Orientation can be upright or inverted, and location is where the image is relative to the mirror, lens, and focal point.
What are ray diagrams in plane mirrors? A ray diagram is a diagram that traces the path that light takes in order for a person to view a point on the image of an object. On the diagram, rays (lines with arrows) are drawn for the incident ray and the reflected ray. Complex objects such as people are often represented by stick figures or arrows.
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What portion of a mirror is required? About half a person's sight is required to see the entire image. In order to determine this, one must draw a ray diagram (rays from the sight to the image's head and toes). Where the rays cross the center line is where the mirror ends are.
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What are right angle mirrors? Right angle mirrors are a pair of plane mirrors that are joined together perpendicularly.
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What are other multiple mirror systems? If two plane mirrors are placed together on one of their edges so as to form a right angle mirror system and then the angle between them is decreased, the number of images that can be seen increases. As the angle between the mirrors approaches 0 degrees (i.e., the mirrors are parallel to each other), the number of images approaches infinity.
Summary Lesson 3 and 4
What are concave mirrors?Concave mirrors are curved. While concave mirrors are on the inside of the sphere, convex mirrors are on the outside of the sphere. If a concave mirror were a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the center of the mirror. This line is known as the principal axis. The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram below. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below. The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram below. The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length (represented by f). Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature. The focal point is the point in space at which light incident towards the mirror and traveling parallel to the principal axis will meet after reflection.
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How is an image formed with a concave mirror?Light always follows the law of reflection, whether the reflection occurs off a curved surface or off a flat surface. Concave mirrors can produce real images and virtual images. The replica is known as the image.
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What are the two rules of reflection for concave mirrors?The image location is the location where all reflected light appears to diverge from. Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.
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How do you draw a ray diagram for concave mirrors?
Pick a point on the top of the object and draw two incident rays traveling towards the mirror.
Once these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors.
Mark the image of the top of the object
Repeat the process for the bottom of the object.
Real images are produced when the object is located a distance greater than one focal length from the mirror. A virtual image is formed if the object is located less than one focal length from the concave mirror. To see why this is so, a ray diagram can be used. What are the image characteristics for concave mirrors? LOST: Case 1: center of curve, inverted, reduced, real image Case 2: center of curve, inverted, normal size, real image Case 3: beyond center of curve, inverted, magnified, real image Case 4: no image Case 5: opposite side of the mirror, upright, magnified, virtual image
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What are the mirror & magnification equations? The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f).
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The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho).
f=+ in a concave mirror f=- in a convex mirror d (image)= + if it is real and on the opposite side of the mirror d (image)= - if it is virtual and located behind the mirror. h (image)= + if the image is upright h (image)= - if the image is inverted
What is spherical aberration? Aberration is a departure from the expected or proper course. Spherical mirrors have an aberration. This defect prohibits the mirror from focusing all the incident light from the same location on an object to a precise point. The defect is most noticeable for light rays striking the outer edges of the mirror. Images from spherical mirrors are often blurry. Any incident ray that strikes the outer edges of the mirror is subject to this departure from the expected or proper course. If a cover is placed over the outer edges of the large demonstration mirror. The result is that the image suddenly becomes more clear and focused. When the problematic portion of the mirror is covered so that it can no longer focus (or mis-focus) light, the image appears more focused. How are images created on convex mirrors? A convex mirror is sometimes referred to as a diverging mirror due to the fact that incident light originating from the same point and will reflect off the mirror surface and diverge. The two rules of reflection for convex mirrors are:
Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in such a manner that its extension will pass through the focal point.
Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.
Summary Lesson 2: Color & Vision
What is the eye's response to visible light? An approximate range of wavelengths is associated with the various perceived colors within the spectrum. Light that enters the eye through the pupil ultimately strikes the inside surface of the eye, the retina. The retina is lined with a variety of light sensing cells known as rods and cones.When light of a given wavelength enters the eye and strikes the cones of the retina, a chemical reaction is activated that results in an electrical impulse being sent along nerves to the brain. It is believed that there are three kinds of cones, each sensitive to its own range of wavelengths within the visible light spectrum. These three kinds of cones are referred to as red cones, green cones, and blue cones because of their respective sensitivity to the wavelengths of light that are associated with red, green and blue. The following is a cone sensitivity curve.
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What are light absorption, reflection, and transmission? Objects have a tendency to selectively absorb, reflect or transmit light certain frequencies. The manner in which visible light interacts with an object is dependent upon the frequency of the light and the nature of the atoms of the object. The selective absorption of light by a particular material occurs because the selected frequency of the light wave matches the frequency at which electrons in the atoms of that material vibrate. Reflection and transmission of light waves occur because the frequencies of the light waves do not match the natural frequencies of vibration of the objects. If the object is transparent, then the vibrations of the electrons are passed on to neighboring atoms through the bulk of the material and reemitted on the opposite side of the object. If the object is opaque, then the vibrations of the electrons are not passed from atom to atom through the bulk of the material. The electrons of atoms on the material's surface vibrate for short periods of time and then reemit the energy as a reflected light wave. If an object absorbs all frequencies of visible light except for the one associated with a particular color, then the object will appear that color. Chemicals that are capable of selectively absorbing one or more frequency of white light are called pigments. What is color addition? Any three colors (or frequencies) of light that produce white light when combined with the correct intensity are called primary colors of light. The most common set of primary colors is red (R), green (G) and blue (B). (R+G+B=W) Yellow, magenta, cyan are secondary colors of light.
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What is color subtraction? The ultimate color appearance of an object is determined by beginning with a single color or mixture of colors and identifying which color or colors of light are subtracted from the original set. (W-B=R+G+B-B=R+G=Y) A pigment that absorbs a single frequency is known as a pure pigment. The color of light absorbed by a pigment is merely the complementary color of that pigment. Thus, pure blue pigments absorb yellow light (which can be thought of as a combination of red and green light). How are blue skies and red sunsets created? Atmospheric nitrogen and oxygen scatter violet light most easily. So as white light from the sun passes through our atmosphere, the high frequencies (BIV) become scattered by atmospheric particles while the lower frequencies (ROY) are most likely to pass through the atmosphere. This scattering of the higher frequencies of light illuminates the skies with light on the BIV end of the visible spectrum. Our eyes are more sensitive to light with blue frequencies. Thus, we view the skies as being blue in color. As the path that sunlight takes through our atmosphere increases in length, ROYGBIV encounters more and more atmospheric particles. This results in the scattering of greater and greater amounts of yellow light. During sunset hours, the light passing through our atmosphere to our eyes tends to be most concentrated with red and orange frequencies of light. For this reason, the sunsets have a reddish-orange hue.
Summary Lesson 1A-F: Refraction at a Boundary
Refraction at a Boundary
A wave will undergo certain behaviors when it encounters the end of the medium. In a wave rope, a portion of the energy carried by the incident pulse is reflected and returns towards the left end of the thin rope. The disturbance that returns to the left after bouncing off the boundary is known as the reflected pulse. A portion of the energy carried by the incident pulse is transmitted into the thick rope. The disturbance that continues moving to the right is known as the transmitted pulse. When passing from air into glass, both the speed and the wavelength decrease. The light is observed to change directions as it crosses the boundary separating the air and the glass. This bending of the path of light is known as refraction. Once the wavefront has passed across the boundary, it travels in a straight line. Refraction is called a boundary behavior.
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Refraction and Sight
Directing of our sight in a specific direction is sometimes referred to as the line of sight. As light travels through a given medium, it travels in a straight line. However, when light passes from one medium into a second medium, the light path bends. The refraction occurs only at the boundary. If when sighting at an object, light from that object changes media on the way to your eye, a visual distortion is likely to occur.
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The Cause of Refraction
There are two conditions that are required in order to observe the change in direction of the path of the students: 1 the students must change speed when crossing the boundary 2. the students must approach the boundary at an angle; refraction will not occur when they approach the boundary head-on (i.e., heading perpendicular to it). Light wave will not undergo refraction if it approaches the boundary in a direction that is perpendicular to it.
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Optical Density and Light Speed
An electromagnetic wave (i.e., a light wave) is produced by a vibrating electric charge. As the wave moves through the vacuum of empty space, it travels at a speed of c (3 x 108 m/s). The speed of the wave depends upon the optical density of that material. The optical density of a material relates to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance. The more optically dense that a material is, the slower that a wave will move through the material. One indicator of the optical density of a material is the index of refraction value (n) of the material.
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Summary Lesson 2A-D: The Mathematics of Refraction
The Angle of Refraction
Refraction is the bending of the path of a light wave as it passes across the boundary separating two media. It is caused by the change in speed experienced by a wave when it changes medium. If a light wave passes from slow medium into a fast medium, then the light would refract away from the normal. If a light wave passes from a fast medium into a slow medium, then the light will refract towards the normal. Wherever the light speed changes most, the refraction is greatest.
Snell's Law
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Ray Tracing and Problem-Solving Snell's Law equation is valued for its predictive ability. When light approaches a layer that has the shape of a parallelogram that is bounded on both sides by the same material, then the angle at which the light enters the material is equal to the angle at which light exits the layer. Determination of n Values Snell's law can be used to identify an unknown material, by finding its index of refraction.
Summary Lesson 3&4: Total Internal Reflection & interesting Refraction Phenomena
Boundary Behavior Revisited At the point of incidence (the point where the incident ray strikes the boundary), a normal line is drawn. The normal line is always drawn perpendicular to the surface at the point of incidence. The normal line creates a variety of angles with the light rays; these angles are important and are given special names. The angle between the incident ray and the normal is the angle of incidence. The angle between the reflected ray and the normal is the angle of reflection. And the angle between the refracted ray and the normal is the angle of refraction. When a light ray reflects off a surface, the angle of incidence is equal to the angle of reflection.
Total Internal Reflection Total internal reflection is the reflection of the total amount of incident light at the boundary between two media. TIR only takes place when the light is in the denser medium and approaching the less dense medium and the angle of incidence is greater than the so-called critical angle. Total internal reflection only occurs with angles larger than the critical angle.
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Fiber Optics
Fiber Optics
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Dispersion of Light By Prisms
The separation of visible light into its different colors is known as dispersion. The angle of deviation is the angle made between the incident ray of light entering the first face of the prism and the refracted ray that emerges from the second face of the prism.
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Rainbow Formation
There are countless paths by which light rays from the sun can pass through a drop. Each path is characterized by this bending towards and away from the normal. One path of great significance in the discussion of rainbows is the path in which light refracts into the droplet, internally reflects, and then refracts out of the droplet. With nonparallel sides, the refraction of light at two boundaries of the droplet results in the dispersion of light into a spectrum of colors. The shorter wavelength blue and violet light refract a slightly greater amount than the longer wavelength red light. Since the boundaries are not parallel to each other, the double refraction results in a distinct separation of the sunlight into its component colors.
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Summary Lesson 5: Refraction The Anatomy of a Lens
A lens is basically a piece of transparent material that refracts light rays in such a way as to form an image. A converging lens is a lens that converges rays of light that are traveling parallel to its principal axis. Converging lenses can be identified by their shape; they are relatively thick across their middle and thin at their upper and lower edges. A diverging lens is a lens that diverges rays of light that are traveling parallel to its principal axis. Diverging lenses can also be identified by their shape; they are relatively thin across their middle and thick at their upper and lower edges.
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Refraction By Lenses Refraction Rules for a Converging Lens: Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.
Refraction Rules for a Diverging Lens: Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point). Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens. Image Formation
Converging lenses can produce both real and virtual images while diverging images can only produce virtual images. The process by which images are formed for lenses is the same as the process by which images are formed for plane and curved mirrors. Real images will appear to upright and to the right of the lens. Diverging lens create virtual images since the refracted rays do not actually converge to a point. In the case of a diverging lens, the image location is located on the object's side of the lens where the refracted rays would intersect if extended backwards.
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Converging Lenses
For ray diagrams, draw one ray from the top of the object through the center. Draw another ray from the top of the object parallel to the principal axis, stop drawing at the origin line, and continue drawing through the focal point. Draw the last ray from the top of the object through F', stop at the origin line, and continue to draw a parallel line to the principal axis. Case 1: the object is located beyond the 2F point: Reduced, Inverted, Real, Between F and 2F
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Case 2: the object is located at the 2F point: Unchanged, inverted, Real, at 2F
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Case 3: the object is located between the 2F point and the focal point (F): Enlarged, Inverted, Realm Beyond 2F
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Case 4: the object is located at the focal point (F): No Image
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Case 5: the object is located in front of the focal point (F): Enlarged, Upright, Virtual, Between F' and 2F'
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Diverging Lenses
For ray diagrams, draw one ray from the top of the object through the center. Draw another ray from the top of the object parallel to the principal axis, stop drawing at the origin line, and continue drawing through the focal point. Draw the last ray from the top of the object through F', stop at the origin line, and continue to draw a parallel line to the principal axis. In each case, the image is located on the object' side of the lens, a virtual image, an upright image, and reduced in size.
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Mathematics of Lenses
The lens equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho).
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Summary Lesson 6: Refraction
The Anatomy of the Eye
The eye is essentially an opaque eyeball filled with a water-like fluid. In the front of the eyeball is a transparent opening known as the cornea, a thin membrane that has an index of refraction of approximately 1.38 and the dual purpose of protecting the eye and refracting light as it enters the eye. After light passes through the cornea, a portion ofit passes through an opening known as the pupil, the black portion in the middle of the eyeball, which is attributed to the fact that the light that the pupil allows to enter the eye is absorbed on the retina and does not exit the eye. The size of the pupil opening can be adjusted by the dilation of the iris, the colored part of the eye; it is a diaphragm that is capable of stretching and reducing the size of the opening. In bright-light situations, the iris adjusts its size to reduce the pupil opening and limit the amount of light that enters the eye. And in dim-light situations, the iris adjusts so as to maximize the size of the pupil opening and increase the amount of light that enters the eye. Light will then enter the crystalline lens, which has an index of refraction of roughly 1.40 and is able to change its shape and thus serves to fine-tune the vision process. The lens is attached to the ciliary muscles. These muscles relax and contract in order to change the shape of the lens. By carefully adjusting the lenses shape, the ciliary muscles assist the eye in the critical task of producing an image on the back of the eyeball. The inner surface of the eye is known as the retina, which the rods and cones that serve the task of detecting the intensity and the frequency of the incoming light. These rods and cones send nerve impulses to the brain. The network of nerve cells that these impulses travel through is bundled together to form the optic nerve on the very back of the eyeball.
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Image Formation
Most of the refraction occurs at the cornea. The index of refraction of the cornea (1.38) is significantly greater than the index of refraction of the surrounding air. This difference in optical density between the air the corneal material combined with the fact that the cornea has a converging shape is what explains the ability of the cornea to do most of the refracting of incoming light rays. The crystalline lens serves to induce small alterations in the amount of corneal bulge as well as to fine-tune some of the additional refraction that occurs as light passes through the lens material. The bulging shape of the cornea causes it to refract light in a manner to similar to a double convex lens. Since the object is typically located at a point in space more than 2-focal lengths from the "lens," the image will be located somewhere between the focal point of the "lens" and the 2F point. The image will be inverted, reduced in size, and real. Vision is dependent upon the stimulation of nerve impulses by an incoming light rays. Only real images would be capable of producing such a stimulation. The reduction in the size of the image allows the entire image to "fit" on the retina. The fact that the image is inverted poses no problem. Our brain has become accustomed to this and properly interprets the signal as originating from a right-side-up object.
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Accomodation
The ability of the eye to adjust its focal length is known as accommodation. Since a nearby object (small dobject) is typically focused at a further distance, the eye accommodates by assuming a lens shape that has a shorter focal length. This reduction in focal length will cause more refraction of light and serve to bring the image back closer to the cornea/lens system and upon the retinal surface. For nearby objects, the ciliary muscles contract and squeeze the lens into a more convex shape. This increase in the curvature of the lens corresponds to a shorter focal length. On the other hand, a distant object is typically focused at a closer distance. The eye accommodates by assuming a lens shape that has a longer focal length. So for distant objects the ciliary muscles relax and the lens returns to a flatter shape. This decrease in the curvature of the lens corresponds to a longer focal length.
Farsightedness
Farsightedness (hyperopia) is the inability of the eye to focus on nearby objects. The farsighted eye has no difficulty viewing distant objects, but the ability to view nearby objects requires a different lens shape - a shape that the farsighted eye is unable to assume. Subsequently, the farsighted eye is unable to focus on nearby objects. The problem most frequently arises during latter stages in life, as a result of the weakening of the ciliary muscles and/or the decreased flexibility of the lens. These two potential causes leads to the result that the lens of the eye can no longer assume the high curvature that is required to view nearby objects. The cure for the farsighted eye centers around assisting the lens in refracting the light. Since the lens can no longer assume the convex and highly curved shape that is required to view nearby objects, it needs some help. Thus, the farsighted eye is assisted by the use of a converging lens, which will refract light before it enters the eye and subsequently decreases the image distance.
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Nearsightedness
Nearsightedness (myopia) is the inability of the eye to focus on distant objects. The nearsighted eye has no difficulty viewing nearby objects. But the ability to view distant objects requires that the light be refracted less. Nearsightedness will result if the light from distant objects is refracted more than is necessary. The problem is most common as a youth, and is usually the result of a bulging cornea or an elongated eyeball. If the cornea bulges more than its customary curvature, then it tends to refract light more than usual. This tends to cause the images of distant objects to form at locations in front of the retina. Subsequently the images of distant objects form in front of the retina. On the retinal surface, where the light-detecting nerve cells are located, the image is not focused, which causes nerve cells to detect a blurry image. The cure for the nearsighted eye is to equip it with a diverging lens. Since the nature of the problem of nearsightedness is that the light is focused in front of the retina, a diverging lens will serve to diverge light before it reaches the eye. This light will then be converged by the cornea and lens to produce an image on the retina.
Table of Contents
Summary Lesson 1D
What is unpolarized light?-A light wave is an electromagnetic wave that travels through a vacuum. Vibrating electric charges produce light waves. An electromagnetic wave has both an electric and a magnetic component. A light wave that is vibrating in more than one plane is unpolarized light.
What is polarized light and polarization?
-Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming unpolarized light into polarized light is known as polarization. There are four methods: transmission, reflection, refraction, and scattering. In transmission through a Polaroid filter, light emerges with one-half the intensity and with vibrations in a single plane (as unpolarized light). Unpolarized light can also undergo polarization by reflection off of nonmetallic surfaces. Polarization is dependent upon the angle at which the light approaches the surface and upon the material that the surface is made of. Refraction occurs when a beam of light passes from one material into another material. The path of the beam changes its direction at the contact between both materials. The refracted beam acquires some polarization. The polarization occurs in a plane perpendicular to the surface. Polarization also occurs when light is scattered while traveling through a medium. When light strikes the atoms of a material, it will often set the electrons of those atoms into vibration. The vibrating electrons then produce their own electromagnetic wave that is radiated outward in all directions.
Summary Lesson 2A
What are electromagnetic and visible spectra?Electromagnetic waves exist with an enormous range of frequencies, known as the electromagnetic spectrum. Our eyes are sensitive to only the visible light spectrum. Each color is characteristic to a different wavelength; and different wavelengths of light waves will bend varying amounts upon passage through a prism. When all the wavelengths of the visible light spectrum strike your eye at the same time, white is perceived. Visible light - the mix of ROYGBIV - is referred to as white light.
Summary Lesson 1A-D
What is the role of light to sight?Without light, there wouldn’t be sight. We are able to see because light from an object can move through space and reach our eyes.Luminous objects are objects that generate their own light. Illuminated objects are objects that are capable of reflecting light to our eyes. Humans are illuminated objects like the moon.
What is the line of sight?
Directing our sight in a specific direction is known the line of sight. To view an object, one must see along a line at that object; and when you do light will come from that object to your eye along the line of sight. Although this light diverges from the object in a variety of directions, your eye only sees the very small diverging cone of rays that is coming towards it. The light ray approaching the mirror is the incident ray. The light ray that reflects off of the mirror and travels to our rye is the reflected ray. The distance from the mirror to the object (object distance) is equal to the distance from the mirror to the image (image distance).
What is the law of reflection?Behavior of light is very predictable. The normal line divides the angle between the incident ray and the reflected ray into two equal angles.
What is the difference between specular and diffuse reflection?The law of reflection is always observed, regardless of the orientation of the surface. Reflection off of smooth surfaces such as mirrors or a calm body of water leads to specular reflection. Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to diffuse reflection.
Summary Lesson 2
Why is an image formed?
In order to see the image of an object in a mirror, you must sight at the image; when you sight at the image, light will come to your eye along that line of sight. The image location is thus located at that position where observers are sighting when viewing the image of an object. It is the location behind the mirror where all the light appears to diverge from.
What are image characteristics in plane mirrors?
Characteristics include type, size, orientation, location. Type can either be real or virtual, real being the actually light where it seems to be and virtual being behind the mirror or in front of the lens. Size can be enlarged, unchanged, or reduced. Orientation can be upright or inverted, and location is where the image is relative to the mirror, lens, and focal point.
What are ray diagrams in plane mirrors?
A ray diagram is a diagram that traces the path that light takes in order for a person to view a point on the image of an object. On the diagram, rays (lines with arrows) are drawn for the incident ray and the reflected ray. Complex objects such as people are often represented by stick figures or arrows.
What portion of a mirror is required?
About half a person's sight is required to see the entire image. In order to determine this, one must draw a ray diagram (rays from the sight to the image's head and toes). Where the rays cross the center line is where the mirror ends are.
What are right angle mirrors?
Right angle mirrors are a pair of plane mirrors that are joined together perpendicularly.
What are other multiple mirror systems?
If two plane mirrors are placed together on one of their edges so as to form a right angle mirror system and then the angle between them is decreased, the number of images that can be seen increases. As the angle between the mirrors approaches 0 degrees (i.e., the mirrors are parallel to each other), the number of images approaches infinity.
Summary Lesson 3 and 4
What are concave mirrors?Concave mirrors are curved. While concave mirrors are on the inside of the sphere, convex mirrors are on the outside of the sphere. If a concave mirror were a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the center of the mirror. This line is known as the principal axis. The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram below. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below. The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram below. The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length (represented by f). Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature. The focal point is the point in space at which light incident towards the mirror and traveling parallel to the principal axis will meet after reflection.How is an image formed with a concave mirror?Light always follows the law of reflection, whether the reflection occurs off a curved surface or off a flat surface. Concave mirrors can produce real images and virtual images. The replica is known as the image.
What are the two rules of reflection for concave mirrors?The image location is the location where all reflected light appears to diverge from. Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.
How do you draw a ray diagram for concave mirrors?
- Pick a point on the top of the object and draw two incident rays traveling towards the mirror.
- Once these incident rays strike the mirror, reflect them according to the two rules of reflection for concave mirrors.
- Mark the image of the top of the object
- Repeat the process for the bottom of the object.
Real images are produced when the object is located a distance greater than one focal length from the mirror. A virtual image is formed if the object is located less than one focal length from the concave mirror. To see why this is so, a ray diagram can be used.What are the image characteristics for concave mirrors?
LOST:
Case 1: center of curve, inverted, reduced, real image
Case 2: center of curve, inverted, normal size, real image
Case 3: beyond center of curve, inverted, magnified, real image
Case 4: no image
Case 5: opposite side of the mirror, upright, magnified, virtual image
What are the mirror & magnification equations?
The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f).
The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho).
f=+ in a concave mirror
f=- in a convex mirror
d (image)= + if it is real and on the opposite side of the mirror
d (image)= - if it is virtual and located behind the mirror.
h (image)= + if the image is upright
h (image)= - if the image is inverted
What is spherical aberration?
Aberration is a departure from the expected or proper course. Spherical mirrors have an aberration. This defect prohibits the mirror from focusing all the incident light from the same location on an object to a precise point. The defect is most noticeable for light rays striking the outer edges of the mirror. Images from spherical mirrors are often blurry.
Any incident ray that strikes the outer edges of the mirror is subject to this departure from the expected or proper course. If a cover is placed over the outer edges of the large demonstration mirror. The result is that the image suddenly becomes more clear and focused. When the problematic portion of the mirror is covered so that it can no longer focus (or mis-focus) light, the image appears more focused.
How are images created on convex mirrors?
A convex mirror is sometimes referred to as a diverging mirror due to the fact that incident light originating from the same point and will reflect off the mirror surface and diverge. The two rules of reflection for convex mirrors are:
- Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in such a manner that its extension will pass through the focal point.
Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.Summary Lesson 2: Color & Vision
What is the eye's response to visible light?
An approximate range of wavelengths is associated with the various perceived colors within the spectrum. Light that enters the eye through the pupil ultimately strikes the inside surface of the eye, the retina. The retina is lined with a variety of light sensing cells known as rods and cones.When light of a given wavelength enters the eye and strikes the cones of the retina, a chemical reaction is activated that results in an electrical impulse being sent along nerves to the brain. It is believed that there are three kinds of cones, each sensitive to its own range of wavelengths within the visible light spectrum. These three kinds of cones are referred to as red cones, green cones, and blue cones because of their respective sensitivity to the wavelengths of light that are associated with red, green and blue. The following is a cone sensitivity curve.
What are light absorption, reflection, and transmission?
Objects have a tendency to selectively absorb, reflect or transmit light certain frequencies. The manner in which visible light interacts with an object is dependent upon the frequency of the light and the nature of the atoms of the object. The selective absorption of light by a particular material occurs because the selected frequency of the light wave matches the frequency at which electrons in the atoms of that material vibrate. Reflection and transmission of light waves occur because the frequencies of the light waves do not match the natural frequencies of vibration of the objects. If the object is transparent, then the vibrations of the electrons are passed on to neighboring atoms through the bulk of the material and reemitted on the opposite side of the object. If the object is opaque, then the vibrations of the electrons are not passed from atom to atom through the bulk of the material. The electrons of atoms on the material's surface vibrate for short periods of time and then reemit the energy as a reflected light wave. If an object absorbs all frequencies of visible light except for the one associated with a particular color, then the object will appear that color. Chemicals that are capable of selectively absorbing one or more frequency of white light are called pigments.
What is color addition?
Any three colors (or frequencies) of light that produce white light when combined with the correct intensity are called primary colors of light. The most common set of primary colors is red (R), green (G) and blue (B). (R+G+B=W) Yellow, magenta, cyan are secondary colors of light.
What is color subtraction?
The ultimate color appearance of an object is determined by beginning with a single color or mixture of colors and identifying which color or colors of light are subtracted from the original set. (W-B=R+G+B-B=R+G=Y) A pigment that absorbs a single frequency is known as a pure pigment. The color of light absorbed by a pigment is merely the complementary color of that pigment. Thus, pure blue pigments absorb yellow light (which can be thought of as a combination of red and green light).
How are blue skies and red sunsets created?
Atmospheric nitrogen and oxygen scatter violet light most easily. So as white light from the sun passes through our atmosphere, the high frequencies (BIV) become scattered by atmospheric particles while the lower frequencies (ROY) are most likely to pass through the atmosphere. This scattering of the higher frequencies of light illuminates the skies with light on the BIV end of the visible spectrum. Our eyes are more sensitive to light with blue frequencies. Thus, we view the skies as being blue in color. As the path that sunlight takes through our atmosphere increases in length, ROYGBIV encounters more and more atmospheric particles. This results in the scattering of greater and greater amounts of yellow light. During sunset hours, the light passing through our atmosphere to our eyes tends to be most concentrated with red and orange frequencies of light. For this reason, the sunsets have a reddish-orange hue.
Summary Lesson 1A-F: Refraction at a Boundary
Refraction at a BoundaryA wave will undergo certain behaviors when it encounters the end of the medium. In a wave rope, a portion of the energy carried by the incident pulse is reflected and returns towards the left end of the thin rope. The disturbance that returns to the left after bouncing off the boundary is known as the reflected pulse. A portion of the energy carried by the incident pulse is transmitted into the thick rope. The disturbance that continues moving to the right is known as the transmitted pulse. When passing from air into glass, both the speed and the wavelength decrease. The light is observed to change directions as it crosses the boundary separating the air and the glass. This bending of the path of light is known as refraction. Once the wavefront has passed across the boundary, it travels in a straight line. Refraction is called a boundary behavior.
Refraction and Sight
Directing of our sight in a specific direction is sometimes referred to as the line of sight. As light travels through a given medium, it travels in a straight line. However, when light passes from one medium into a second medium, the light path bends. The refraction occurs only at the boundary. If when sighting at an object, light from that object changes media on the way to your eye, a visual distortion is likely to occur.
The Cause of Refraction
There are two conditions that are required in order to observe the change in direction of the path of the students: 1 the students must change speed when crossing the boundary 2. the students must approach the boundary at an angle; refraction will not occur when they approach the boundary head-on (i.e., heading perpendicular to it). Light wave will not undergo refraction if it approaches the boundary in a direction that is perpendicular to it.
Optical Density and Light Speed
An electromagnetic wave (i.e., a light wave) is produced by a vibrating electric charge. As the wave moves through the vacuum of empty space, it travels at a speed of c (3 x 108 m/s). The speed of the wave depends upon the optical density of that material. The optical density of a material relates to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance. The more optically dense that a material is, the slower that a wave will move through the material. One indicator of the optical density of a material is the index of refraction value (n) of the material.
Summary Lesson 2A-D: The Mathematics of Refraction
The Angle of RefractionRefraction is the bending of the path of a light wave as it passes across the boundary separating two media. It is caused by the change in speed experienced by a wave when it changes medium. If a light wave passes from slow medium into a fast medium, then the light would refract away from the normal. If a light wave passes from a fast medium into a slow medium, then the light will refract towards the normal. Wherever the light speed changes most, the refraction is greatest.
Snell's Law
Ray Tracing and Problem-Solving
Snell's Law equation is valued for its predictive ability. When light approaches a layer that has the shape of a parallelogram that is bounded on both sides by the same material, then the angle at which the light enters the material is equal to the angle at which light exits the layer.
Determination of n Values
Snell's law can be used to identify an unknown material, by finding its index of refraction.
Summary Lesson 3&4: Total Internal Reflection & interesting Refraction Phenomena
Boundary Behavior RevisitedAt the point of incidence (the point where the incident ray strikes the boundary), a normal line is drawn. The normal line is always drawn perpendicular to the surface at the point of incidence. The normal line creates a variety of angles with the light rays; these angles are important and are given special names. The angle between the incident ray and the normal is the angle of incidence. The angle between the reflected ray and the normal is the angle of reflection. And the angle between the refracted ray and the normal is the angle of refraction. When a light ray reflects off a surface, the angle of incidence is equal to the angle of reflection.
Total Internal Reflection
Total internal reflection is the reflection of the total amount of incident light at the boundary between two media. TIR only takes place when the light is in the denser medium and approaching the less dense medium and the angle of incidence is greater than the so-called critical angle. Total internal reflection only occurs with angles larger than the critical angle.
Dispersion of Light By Prisms
The separation of visible light into its different colors is known as dispersion. The angle of deviation is the angle made between the incident ray of light entering the first face of the prism and the refracted ray that emerges from the second face of the prism.
Rainbow Formation
There are countless paths by which light rays from the sun can pass through a drop. Each path is characterized by this bending towards and away from the normal. One path of great significance in the discussion of rainbows is the path in which light refracts into the droplet, internally reflects, and then refracts out of the droplet. With nonparallel sides, the refraction of light at two boundaries of the droplet results in the dispersion of light into a spectrum of colors. The shorter wavelength blue and violet light refract a slightly greater amount than the longer wavelength red light. Since the boundaries are not parallel to each other, the double refraction results in a distinct separation of the sunlight into its component colors.
Summary Lesson 5: Refraction
The Anatomy of a Lens
A lens is basically a piece of transparent material that refracts light rays in such a way as to form an image. A converging lens is a lens that converges rays of light that are traveling parallel to its principal axis. Converging lenses can be identified by their shape; they are relatively thick across their middle and thin at their upper and lower edges. A diverging lens is a lens that diverges rays of light that are traveling parallel to its principal axis. Diverging lenses can also be identified by their shape; they are relatively thin across their middle and thick at their upper and lower edges.
Refraction By Lenses
Refraction Rules for a Converging Lens: Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.
Refraction Rules for a Diverging Lens: Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point). Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.
Image Formation
Converging lenses can produce both real and virtual images while diverging images can only produce virtual images. The process by which images are formed for lenses is the same as the process by which images are formed for plane and curved mirrors. Real images will appear to upright and to the right of the lens. Diverging lens create virtual images since the refracted rays do not actually converge to a point. In the case of a diverging lens, the image location is located on the object's side of the lens where the refracted rays would intersect if extended backwards.
Converging Lenses
For ray diagrams, draw one ray from the top of the object through the center. Draw another ray from the top of the object parallel to the principal axis, stop drawing at the origin line, and continue drawing through the focal point. Draw the last ray from the top of the object through F', stop at the origin line, and continue to draw a parallel line to the principal axis.
Case 1: the object is located beyond the 2F point: Reduced, Inverted, Real, Between F and 2F
Case 2: the object is located at the 2F point: Unchanged, inverted, Real, at 2F
Case 3: the object is located between the 2F point and the focal point (F): Enlarged, Inverted, Realm Beyond 2F
Case 4: the object is located at the focal point (F): No Image
Case 5: the object is located in front of the focal point (F): Enlarged, Upright, Virtual, Between F' and 2F'
Diverging Lenses
For ray diagrams, draw one ray from the top of the object through the center. Draw another ray from the top of the object parallel to the principal axis, stop drawing at the origin line, and continue drawing through the focal point. Draw the last ray from the top of the object through F', stop at the origin line, and continue to draw a parallel line to the principal axis. In each case, the image is located on the object' side of the lens, a virtual image, an upright image, and reduced in size.
Mathematics of Lenses
The lens equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho).
Summary Lesson 6: Refraction
The Anatomy of the Eye
The eye is essentially an opaque eyeball filled with a water-like fluid. In the front of the eyeball is a transparent opening known as the cornea, a thin membrane that has an index of refraction of approximately 1.38 and the dual purpose of protecting the eye and refracting light as it enters the eye. After light passes through the cornea, a portion ofit passes through an opening known as the pupil, the black portion in the middle of the eyeball, which is attributed to the fact that the light that the pupil allows to enter the eye is absorbed on the retina and does not exit the eye. The size of the pupil opening can be adjusted by the dilation of the iris, the colored part of the eye; it is a diaphragm that is capable of stretching and reducing the size of the opening. In bright-light situations, the iris adjusts its size to reduce the pupil opening and limit the amount of light that enters the eye. And in dim-light situations, the iris adjusts so as to maximize the size of the pupil opening and increase the amount of light that enters the eye. Light will then enter the crystalline lens, which has an index of refraction of roughly 1.40 and is able to change its shape and thus serves to fine-tune the vision process. The lens is attached to the ciliary muscles. These muscles relax and contract in order to change the shape of the lens. By carefully adjusting the lenses shape, the ciliary muscles assist the eye in the critical task of producing an image on the back of the eyeball. The inner surface of the eye is known as the retina, which the rods and cones that serve the task of detecting the intensity and the frequency of the incoming light. These rods and cones send nerve impulses to the brain. The network of nerve cells that these impulses travel through is bundled together to form the optic nerve on the very back of the eyeball.
Image Formation
Most of the refraction occurs at the cornea. The index of refraction of the cornea (1.38) is significantly greater than the index of refraction of the surrounding air. This difference in optical density between the air the corneal material combined with the fact that the cornea has a converging shape is what explains the ability of the cornea to do most of the refracting of incoming light rays. The crystalline lens serves to induce small alterations in the amount of corneal bulge as well as to fine-tune some of the additional refraction that occurs as light passes through the lens material. The bulging shape of the cornea causes it to refract light in a manner to similar to a double convex lens. Since the object is typically located at a point in space more than 2-focal lengths from the "lens," the image will be located somewhere between the focal point of the "lens" and the 2F point. The image will be inverted, reduced in size, and real. Vision is dependent upon the stimulation of nerve impulses by an incoming light rays. Only real images would be capable of producing such a stimulation. The reduction in the size of the image allows the entire image to "fit" on the retina. The fact that the image is inverted poses no problem. Our brain has become accustomed to this and properly interprets the signal as originating from a right-side-up object.
Accomodation
The ability of the eye to adjust its focal length is known as accommodation. Since a nearby object (small dobject) is typically focused at a further distance, the eye accommodates by assuming a lens shape that has a shorter focal length. This reduction in focal length will cause more refraction of light and serve to bring the image back closer to the cornea/lens system and upon the retinal surface. For nearby objects, the ciliary muscles contract and squeeze the lens into a more convex shape. This increase in the curvature of the lens corresponds to a shorter focal length. On the other hand, a distant object is typically focused at a closer distance. The eye accommodates by assuming a lens shape that has a longer focal length. So for distant objects the ciliary muscles relax and the lens returns to a flatter shape. This decrease in the curvature of the lens corresponds to a longer focal length.
Farsightedness
Farsightedness (hyperopia) is the inability of the eye to focus on nearby objects. The farsighted eye has no difficulty viewing distant objects, but the ability to view nearby objects requires a different lens shape - a shape that the farsighted eye is unable to assume. Subsequently, the farsighted eye is unable to focus on nearby objects. The problem most frequently arises during latter stages in life, as a result of the weakening of the ciliary muscles and/or the decreased flexibility of the lens. These two potential causes leads to the result that the lens of the eye can no longer assume the high curvature that is required to view nearby objects. The cure for the farsighted eye centers around assisting the lens in refracting the light. Since the lens can no longer assume the convex and highly curved shape that is required to view nearby objects, it needs some help. Thus, the farsighted eye is assisted by the use of a converging lens, which will refract light before it enters the eye and subsequently decreases the image distance.
Nearsightedness
Nearsightedness (myopia) is the inability of the eye to focus on distant objects. The nearsighted eye has no difficulty viewing nearby objects. But the ability to view distant objects requires that the light be refracted less. Nearsightedness will result if the light from distant objects is refracted more than is necessary. The problem is most common as a youth, and is usually the result of a bulging cornea or an elongated eyeball. If the cornea bulges more than its customary curvature, then it tends to refract light more than usual. This tends to cause the images of distant objects to form at locations in front of the retina. Subsequently the images of distant objects form in front of the retina. On the retinal surface, where the light-detecting nerve cells are located, the image is not focused, which causes nerve cells to detect a blurry image. The cure for the nearsighted eye is to equip it with a diverging lens. Since the nature of the problem of nearsightedness is that the light is focused in front of the retina, a diverging lens will serve to diverge light before it reaches the eye. This light will then be converged by the cornea and lens to produce an image on the retina.